Polynomial splittings of metabelian von Neumann rho-invariants

2007/10/10 by Se-Goo Kim, Kim, Se-Goo, Taehee Kim +1
Mathematics · #57M25 (Primary) 57N70 (Secondary) #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M25 #msc:57N70

paper · pdf · doi:10.48550/arxiv.0710.1929

8 pages, 1 figure

arxiv created 2007/10/10 · openalex publication_date 2007/10/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if the connected sum of two knots with coprime Alexander polynomials has vanishing von Neumann rho-invariants associated with certain metabelian representations then so do both knots. As an application, we give a new example of an infinite family of knots which are linearly independent in the knot concordance group.

Citations

• Knot concordance, Whitney towers and L 2 -signatures

Related

• Primary decomposition of knot concordance and von Neumann rho-invariants
• Knots having the same Seifert form and primary decomposition of knot concordance
• Polynomial splittings of Casson-Gordon invariants
• Infinite family of non-concordant knots having the same Seifert form
• Higher dimensional twisted Alexander polynomials for metabelian representations